Operator system

Given a unital C*-algebra ${𝒜}$, a *-closed subspace S containing 1 is called an operator system. One can associate to each subspace ${ℳ}\subseteq {𝒜}$ of a unital C*-algebra an operator system via $S:={ℳ}+{{ℳ}}^{*}+\mathbb{ℂ}1$.

The appropriate morphisms between operator systems are completely positive maps.

By a theorem of Choi and Effros, operator systems can be characterized as *-vector spaces equipped with an Archimedean matrix order.

See also

• Operator space